Sunday, November 8, 2020

Checking Out the QI Model

 

  There was a lot of interest in "curve flattening" but the fits don't appear to show much evidence of any. There does appear to be a little lowering near the peak but could it have been due to the testing labs being overwhelmed by the number of cases and confirmations being delayed?



The best fit of Q/I for λ helped give the best fit for the QI model although the initial values for K and I required for the numerical integration of the dI/dt formula were somewhat unexpected. The observed values of K were used in the calculations.







Again there appears to be lower values around the peak in the Q/I plot. The time is the number of days from 4/1/20 and the initial observed values for K are lower than those required by the model fit. One could ask if this is due a lack of test kits or maybe poor statistics for a lower number of cases?


The formula for Q seems to indicate that the infection rate is proportional to the number of daily new cases and a factor which includes a rate which decreases as the number of known cases increases as well as a negative term similar to the removal rate in the SIR model. The exponential term appears to be an indication of a saturation effect with the number of uninfected individuals around in infected individual decreasing over time.


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